Confidence interval and reliability factor

[kaia_p]

Hi, please help to explain how is reliability factor derived? Is there a formula for that or should just know the below values?
Point estimate ± Reliability factor × Standard error
90 percent confidence intervals: Use z0.05 = 1.65 95 percent confidence intervals: Use z0.025 = 1.96 99 percent confidence intervals: Use z0.005 = 2.58

 

[S2000magician]

You get the reliability factor from a z-table or a t-table. For example, if you want a 90% confidence interval, then you have 90% in the center, 5% in left tail, and 5% in the right tail. If you look at a z-table (for negative values of z), and sift through the table for a value of 5% (0.0500), you’ll find that the corresponding z-value is half-way between -1.64 and -1.65; call it -1.645. If you look at a z-table (for positive values of z), and sift through the table for a value of 95% (0.9500, which is 1 – 0.0500), you’ll find that the corresponding z-value is half-way between +1.64 and +1.65; call it +1.645.